How do you figure out what a person's uncorrected visual acuity is,
expressed as 20/x, if the person's corrected visual acuity is 20/20,
and you know the person's prescription?  For example, if my eyes are
correctible to 20/20 with -8.0 diopter lenses (that is, lenses with
focal length -12.5 cm), how well do I see without glasses?  20/1000 or
what?  There are online references that say there is no exact
relationship.  There must be at least an approximate
relationship--what is it?

Hello, racecar.

It's true that the 20/something numbers associated with the Snellen
visual acuity chart do not have precise equivalents in diopters. I
squabbled with an ophthalmologist about this many years ago. I asked
him for my exact "20/something" number, and he gave me a bunch of
rigmarole which basically translated to "I dunno." As it turns out, "I
dunno" was the right answer; visual acuity is affected by several
factors in addition to the curvature of the eye's lens. I finally
wrung a guesstimate out of an optometrist, who said that my correction
of -7.75 diopters was in the vicinity of 20/1000. He may have pulled
this out of his navel, of course, but it seems to jibe with what I've
learned elsewhere.

I have found a chart that gives some rough approximations of
"20/something" values for myopic (nearsighted) patients:

"Eyesight is commonly evaluated by reading a Snellen eye chart from a
distance of 20 feet - the distance beyond which the lens does not need
to adjust for distance. (This is the equivalent of the infinity
setting on a camera.) Variances from the 'ideal' 20/20 can be caused
by myopia, astigmatism and other variables including the lighting in
the room. 20/something provides a descriptive approximation of visual
acuity.
 
The power of a lens placed in front of the eye to correct for myopia
is measured in terms of diopters. Diopters are a prescriptive measure
of myopia. If myopia is the only variable, the following approximate
relationships exist between measurements in terms of diopters and in
terms of 20/something:

In Diopters     20/something 
-------------------------------
  -0.50         20/25 to 20/30 
  -1.00         20/30 to 20/50 
  -3.00         20/300 
  -4.00         20/400 
  -5.00         20/600 
  -6.00         20/800 "

LPF: Diopters and 20/Something
http://www.lpf.com/source/rk/20something.html

My Google search strategy:

Google Web Search: 20/100 20/200 diopters
://www.google.com/search?hl=en&q=20%2F100+20%2F200+diopters

I hope this is precisely what you need. If it is not, please request
clarification, and I'll resume the quest.

Best regards,
pinkfreud